Radar Cross Section Based Statistical Recognition of UAVs at Microwave Frequencies
Martins Ezuma, Chethan Kumar Anjinappa, Mark Funderburk, Ismail Guvenc
11 Radar Cross Section Based StatisticalRecognition of UAVs at MicrowaveFrequencies
Martins Ezuma, Chethan Kumar Anjinappa, Mark Funderburk, and Ismail Guvenc
Abstract
This paper presents a radar cross-section (RCS)-based statistical recognition system for identify-ing/classifying unmanned aerial vehicles (UAVs) at microwave frequencies. First, the paper presentsthe results of the vertical (VV) and horizontal (HH) polarization RCS measurement of six commercialUAVs at 15 GHz and 25 GHz in a compact range anechoic chamber. The measurement results showthat the average RCS of the UAVs depends on shape, size, material composition of the target UAVas well as the azimuth angle, frequency, and polarization of the illuminating radar. Afterward, radarcharacterization of the target UAVs is achieved by fitting the RCS measurement data to 11 differentstatistical models. From the model selection analysis, we observe that the lognormal, generalized extremevalue, and gamma distributions are most suitable for modeling the RCS of the commercial UAVs whilethe Gaussian distribution performed relatively poorly. The best UAV radar statistics forms the classconditional probability densities for the proposed UAV statistical recognition system. The performanceof the UAV statistical recognition system is evaluated at different signal noise ratio (SNR) with the aidof Monte Carlo analysis. At an SNR of 10 dB, the average classification accuracy of 97.43% or betteris achievable.
Index Terms
Akaike information criterion (AIC), automatic target recognition (ATR), Bayesian informationcriterion (BIC), classification, compact-range chamber, detection, RCS, UAV.
This work has been supported in part by the National Aeronautics and Space Administration (NASA) under the Federal AwardID number NNX17AJ94A. a r X i v : . [ ee ss . SP ] F e b I. I
NTRODUCTION
Civilian unmanned aerial vehicle (UAV) technology is a disruptive technology that has thepotential to transform modern society. However, there are challenges to be overcome beforeUAVs can be effectively integrated into the national airspace. The most common challenge issecurity and privacy. For instance, recently UAVs have been used to carry out crimes and terrorattacks that threaten public safety [1]. Therefore, there have been calls to investigate effectiveways to detect, classify, and interdict small commercial UAVs [2].Radar-based solutions have become appealing for UAV detection and recognition. This isbecause radars can operate effectively even in adverse weather such as fog, rain, and snow. Asopposed to computer vision based approaches, radars can operate at night time. Moreover, radarscan be easily deployed on different platforms on land, sea, and air. Active radars detect objectsby illuminating them with electromagnetic energy and listening for the echo (back-scatteredsignals) from the targets. Although radar-based UAV detection is important, it is also desirableto be able to recognize and classify targets of interest.The radar cross section (RCS) provides a measure of the target’s reflectivity, and most complextargets have unique RCS signature that can be used as the basis for target identification. The RCSsignature can be used to distinguish a target from clutters. As an example, since most commercialUAVs fly at low-altitude, surveillance radars have to be tilted to low-grazing angles to search forUAVs. However, at low grazing angles, the surveillance radar could easily confuse reflections(scattering) from ground clutters and small birds with the radar return from a UAV [3], [4]. Toavoid such confusion, we can create a database of RCS signature of specific UAVs of interest.This will be useful in designing automatic target recognition (ATR) and knowledge-based (KB)radar systems that use the prior knowledge of the scattering characteristics of specific targets [5].In most of the studies on UAV RCS measurements, only the measured RCS results areprovided. Extensive statistical modeling and RCS-based UAV classification of these commercialUAVs have not been investigated to our best knowledge. Motivated by the gaps in the existingliterature, our contributions in this work can be summarized as follows.1) We report the results of the RCS measurement of six popular commercial UAVs in acompact range anechoic chamber at 15 GHz and 25 GHz. The choice of 15 GHz and 25GHz for the UAV RCS measurement is mainly informed by the trend in the commercialcounter-UAV radar industry and academic research. For example, Fortem Technologies and
Ancortek Inc. are providing UAV radar solutions at 15 GHz and 25 GHz respectively [6],[7]. We describe in detail the chamber setup and the measurement procedure. Unlike theindoor near field range [8], [9], which does not satisfy the far-field condition for generatingplane wave illumination for RCS measurement, the indoor compact range measurementsetup uses a large parabolic reflector to ensure the target UAV is illuminated by planewaves and thus fulfilling the Fraunhofer far-field requirement.2) We provide extensive statistical analysis of the measured RCS data using the maximumlikelihood estimator, Akaike information criterion (AIC), and the Bayesian informationcriterion (BIC). Using these statistical tools, we estimate the best statistical parametricmodels for each UAV type. For each UAV type, the best statistical model is selectedfrom a set of 11 candidate models. Then, we rank the models according to their AIC andBIC scores with the best statistical model having the least AIC or BIC score. Also, weinvestigate the effect of frequency and polarization on the goodness of fit of the statisticaldistributions.3) We proposed an RCS-based statistical recognition/classification for commercial UAVs. TheUAV recognition system estimates the likelihood that a given test RCS data captured froman unknown UAV belongs to one of the UAV types or classes contained in the database.In the database, each UAV type is described by the most appropriate statistical distributionselected by either the AIC and BIC criteria. We analyzed the classification results withthe aid of the Monte Carlo analysis. We investigated the effects of SNR, frequency, andpolarization on the classification accuracy. At 10 dB SNR, using the 15 GHz and 25 GHzHH-polarized RCS test data, the UAV recognition system achieves an average accuracyof 97.43% and 100%, respectively. Similarly, for the 15 GHz VV-polarized test data, theaverage classification accuracy is 99.17% at 10 dB SNR. We provide confusion matricesto investigate the strengths and weaknesses of the recognition system.In an earlier work [10], we presented the VV-polarized RCS measurement data from threeUAVs in a compact range anechoic chamber setup. In the current study, we provide the VVand HH-polarized RCS measurement data for six common UAVs. That way, we can investigateand compare the effects of polarization on the UAV RCS measurement results. Besides, in thisstudy, we provide a detailed explanation of the background subtraction and calibration techniqueemployed in our post-processing. UAV classification problem is not studied in [10], which is a major focus of the present work.The remainder of the paper is organized as follows: Section II provides a brief literatureoverview of UAV RCS measurements and radar-based UAV detection/classification. Section IIIexplains the basic principles of RCS measurement in both indoor and outdoor settings. Section IVdescribes the measurement procedure while Section V describes the statistical analysis and modelselection techniques employed. Section VI presents the measurement and numerical results andSection VII concludes the paper. II. L
ITERATURE O VERVIEW
The process of classifying or identifying a radar target often requires the exploitation of anyinformation imprinted on the scattered signals from the target (target echo). An example isthe use of radar micro-Doppler analysis and inverse synthetic aperture radar (ISAR) imagingfor UAV identification [3], [11]–[13]. It is known that complex objects like UAVs consist ofseveral components, each with unique individual motion dynamics. For example, the rotatingpropellers (micromotion) have different dynamics from the mainframe. Therefore, the incomingelectromagnetic wave will be modulated differently by the individual components of the UAV,thus producing different Doppler shifts. Therefore, using joint time-frequency spectral analysison the returned signal, the features of the UAVs can be identified. In [3], micro-Doppler analysisis used to distinguish a UAV from a walking man. In [11], [12], micro-Doppler analysis is used todistinguish drones from birds. In [13], features extracted from micro-Doppler signatures are usedto discriminate between loaded and unloaded micro-drones. The study shows that the Dopplercentroid and Doppler bandwidth were more suitable for drone identification as compared to thesingular value decomposition (SVD). However, a major drawback in using micro-Doppler foridentifying targets is the requirement of wide bandwidth and high computational resources [14].A large bandwidth signal is needed to generate high-resolution micro-Doppler images. Also,currently, there are no effective algorithms for decomposing a complex micro-Doppler signatureinto physical component-based mono-component signatures [15]. This makes it difficult for amachine to accurately track and identify multicomponent micro-Doppler signatures without anyhuman observer [15]. Also, due to the requirement of the Nyquist-Shannon theory, to resolvethe micro-Doppler signatures of a rotating propeller, the pulse repetition frequency (PRF) of aradar needs to be at least four times the maximum Doppler shift induced by the propellers [15].This requirement could pose a design challenge for surveillance radars, especially those used in airports [16]. Besides, due to the small dimensions of many drones, a larger signal-to-noise ratio (SNR) is required for a radar to capture the micro-Doppler modulations of itsrotating propellers [16]. Furthermore, since Doppler radars can only measure radial velocity, itis impossible to perform micro-Doppler velocity if the target UAV has no radial velocity relativeto the radar. Also, if there are no oscillations/rotations or vibrations, it is almost impossibleto extract any micro-Doppler signature from a target. Therefore an aircraft without rotatingpropellers cannot be identified using micro-Doppler signature techniques.On the other hand, ISAR is a standard radar mode for high-resolution radar target identification.The ISAR images are generated by using short pulses to obtain high range resolution andexploiting the target motion to obtain high-resolution cross-range [17]. This requires 2D or 3Dinverse Fourier transform operations. The ISAR images show the signature features of the UAVand the dominant scattering centers. In [18], [19], 2D ISAR images of several consumer droneswere generated. However, a key challenge of ISAR imaging is that blind motion compensationis required to form a focused image of the moving UAV [20]. That is if the object has complexmotion, such as non-uniform pitching, rolling, and yawing as in the case of drones, this cangreatly degrade the ISAR images [17], [21], Also, ISAR imaging requires wide bandwidth andhigh computational resources [14]. Therefore, in this study, our focus is the 1-D radar cross-section (RCS) signature of UAVs which can be obtained with lower demand on radar memoryand processing resources. RCS measurement does not require high-energy/high-resolution radarpulse waveform, and hence considered in several works in the literature for target identification,association, and tracking [22], [23]. RCS data can also be used jointly with other approaches toimprove the detection/classification accuracy.In recent times, there have been a few measurement campaigns to ascertain the RCS ofsome commercial UAVs. The RCS measurement can be carried out both in outdoor and indoorenvironments. The advantage of the outdoor measurement (outdoor range) is the ease of capturingreflections from the target UAV at far-field (plane-wave illumination). This is necessary sinceradar detection performance is evaluated at the far-field condition. However, in outdoor measure-ment scenarios, reflections from the ground, and other clutter in the environment are difficult toeliminate [24]. This makes it very difficult and sometimes impossible to accurately determine theactual reflections (RCS) from the target itself. Moreover, the effects of ground clutter reflectionsare stronger when measuring the RCS of low-altitude targets such as commercial UAVs. Besides,the most advanced outdoor RCS measurement ranges are controlled by the military such as the secret Etcheron Valley Junction Ranch RCS Range operated by the United States Navy and theLockheed Martin Helendale RCS facility. These facilities are considered classified test sites andthus not available for academic research. These military-controlled facilities are often located inremote valleys or desert environments with no building, pedestrian, automobile, and poles. This isto ensure that clutters and multipath reflections are avoided. In these outdoor ranges, commercialor military grade radars are used to illuminate the target object. The scattered signals from theobject are captured by the radar receiver and used to estimate the target RCS. Furthermore,RCS measurement calibration is done using standard objects with known RCS such as a sphere,cylinder, trihedral, or dihedral Corner Reflector [25]. As a result of the challenges with outdoorRCS measurement, recent studies on UAV RCS measurements have focused on the controlledindoor environment (indoor ranges), which is the focus of the current study.Use of RCS has also been used in the literature to distinguish small UAVs from birds. In [26],the in-flight RCS of several birds (clutter) and UAVs are measured using K-band and W-bandradars. The study shows that the measured RCS values of drones and birds are close. However,drones and birds could be distinguished by their RCS statistical distributions. In [27], an ATRsystem was designed to distinguish birds from UAVs using Ku-band radar echo. In [28], the flightmodes of a bird (gliding and flapping) are recognized using the wing RCS signature. In [29],the RCS of birds is measured around airports and this information is used to provide situationawareness for manned aircraft. In [30], an avian radar is used for drone and bird detection. Fordetection, the avian radar exploits the RCS statistical model of the targets. We have recently beenworking on collecting measurement data from birds and drones, for distinguishing one from theother, using the TrueView radar from Fortem Technology [6]. Therefore, the techniques describedin this study can be used to identify UAVs as well as distinguish between UAVs and birds.However, due to space limitations and different contexts, we will report our results with birdsin our future work. Therefore, the current study will only focus on multiple UAV identification.We will not consider the RCS-based classification of birds and other non-UAV targets.Table I provides a brief survey of recent studies on the RCS measurement of commercial UAVs.In these controlled indoor measurement setups, the effect of clutters and ground reflections canbe readily solved. Almost all indoor RCS measurements are carried out in an anechoic chamberwhere the walls, ceilings and floors are laced with high-fidelity radar absorption materials(RAM). The RAM lacing ensures that reflections from background clutter are minimized asmuch as possible. However, unlike outdoor environments, generating the far-field measurement
TABLE IL
ITERATURE R EVIEW OF C IVILIAN
UAV RCS M
EASUREMENT AND S TATISTICAL A NALYSIS .Ref. Frequency Measurement range of UAVs Background Polarization RCS Statistical RCS-based(GHz) subtraction model selection UAV Clas-sification[31] 8.75 Outdoor (open range) 1 (cid:55) (cid:55) (cid:55) [26] 24, 94 Outdoor (open range) 3 (cid:55) CP (cid:55) (cid:55) [27] 12-18 Outdoor (open range) 1 (cid:55) (cid:55) (cid:55) [8] 9.5 Indoor (near field range) 1 (cid:55) (cid:55) (cid:55) [32] 2.4, 24 Indoor (near field range) 1 (cid:55) H-H (cid:55) (cid:55) [33] 60, 79 Indoor (near field range) 1 (cid:55)
H-H (cid:55) (cid:55) [34] 24/26 Indoor/Outdoor 5 (cid:55) VV (cid:55) (cid:55) [18] 3-6, 12-15 Indoor (near field range) 3 (cid:88) VV, HH (cid:55) (cid:55) [19] 8, 12 Indoor (near field range) 2 (cid:88)
VV, HH (cid:88) (cid:55) [35] 9 Indoor (near field range) 1 (cid:55) HH (cid:55) (cid:55) [36] 26-40 Indoor (near field range) 9 (cid:55) VV, HH (cid:55) (cid:55) [9] 8–10 Indoor (near field range) 1 (cid:88) VV (cid:88) (cid:55) [10] 15, 25 Indoor (compact range) 3 (cid:88) VV (cid:88) (cid:55) Currentwork 15, 25 Indoor (compact range) 6 (cid:88)
VV, HH, (cid:88) (cid:88) HH, VV, and CP represents the horizontal, vertical, and circular polarization respectively. conditioning in the indoor environment is not trivial, especially at microwave frequencies. Thisis a drawback in most of the indoor measurements surveyed in Table I. Far-field illumination isonly possible if the distance between the radar and the target is at least equal to the Fraunhoferdistance [37]. This is difficult to achieve in almost all indoor UAV RCS measurements atmicrowave frequencies. Therefore, thus far, most indoor RCS measurements can be classifiedas near field measurement and the obtained RCS results are at best only an approximation.Moreover, background subtraction is not implemented in some of these indoor measurementsetups. These omissions would affect the accuracy of the RCS measurement since antennacoupling and multipath reflections in the chamber need to be estimated and eliminated fromthe measurements.
III. P
RINCIPLE OF
RCS M
EASUREMENT
In this section, we present the basic principles and experimental techniques for RCS measure-ments in both outdoor and indoor settings.
A. Theoretical Background
The RCS is a measure of how much power is scattered by a target in a given direction whenilluminated by a radar. The far-field RCS of the target is given by [38]: σ = lim R →∞ πR | E s | | E i | = lim R →∞ πR | H s | | H i | , (1)where σ (m ) is the RCS of the target while E s (V/m) and E i (V/m) are the far field scatteredand incident electric field intensities respectively as seen at a distance R . Also, H s (A/m) and H i (A/m) are the far field scattered and incident magnetic field intensities respectively as seen ata distance R . In terms of the horizontal ( H ) and vertical ( V ) polarization components of E s and E i , the response of the target to the incident wave is described by a × complex backscatteredmatrix equation: E s,H E s , V = 14 πR √ σ HH √ σ VH √ σ HV √ σ VV E i , H E i , V , where σ HH and σ VV are co-polarized RCS of the object while σ HV and σ VH are the cross-polarizedRCS. In the case of backscattering (monostatic and quasi-monostatic), σ HV = σ VH .An RCS measurement setup can be broadly classified into two main groups: outdoor-rangeand indoor-range (near-field and compact-range). These ranges will be explained in the next twosubsections. B. Outdoor RCS Measurement
The RCS definition in (1) requires the physical distance of R between the radar and thetarget UAV to be sufficiently large. This is called the far-field condition and is necessary togenerate plane wave illumination for the target UAV. Besides, the far-field requirements eliminateany distance dependency in the RCS signature of the target [38]. Mathematically, the far-fielddistance (Fraunhofer distance) R is given by: R ≥ D λ , (2) Test Zone D 𝑹 = 𝟐𝑫 𝝀 Plane Wavefronts
Fig. 1. Outdoor RCS measurement scenario of a small UAV. Atmospheric condition and inability to isolate the target are issues. where D is the transverse length (or diameter) of the target and λ is the wavelength of theradar signal [38]. At this distance R , the spherical wavefronts emitted by the radar will haveapproximately equal phases across any measurement area (plane wave fronts). For instance, aDJI Matrice 600 UAV, a popular commercial grade UAV, have diameter of about 1.133 m [39].Therefore, using a 25 GHz radar, we need a separation distance R of at least 213.95 m toaccurately measure the RCS of the UAV in the far-field. This is almost twice the length ofa standard football field. However, in outdoor measurement environment, we can achieve thedesired separation distance in free space. This is the advantage of the outdoor range experiment.During the measurement, the UAV is placed on a Pylon stand or allowed to hover in the radar’sfield of view. Fig. 1 shows a typical outdoor range RCS measurement scenario. However, asshown in Fig. 1, the ground clutter reflection is an unavoidable drawback in outdoor rangeexperiment. Besides, environmental clutters like buildings will generate multipath scatteringwhich will affect the accuracy of the measurement. C. Indoor RCS Measurement
Due to the challenge of ground reflection, environmental clutter, and atmospheric conditionsassociated with outdoor range, RCS measurement of commercial UAVs can be carried out inan indoor environment. In most cases, anechoic chambers are used as a controlled environmentfor indoor RCS measurement. Fig. 2 shows a typical indoor measurement setup. Here, the radarsystem is implemented using a combination of vector network analyzer (VNA), antennas, andpower amplifiers. The consumer UAV is placed on a turntable which is controlled by computer.However, for high-frequency measurement, say 25 GHz, the far-field distance requirement is Test Zone
Control Computer
Amplifier
VNA
Tx Ant.
Rx Ant.
Fig. 2. Indoor near field RCS measurement. Spherical waves are used to illuminate the target. difficult to achieve within an indoor experimental setup. It will be too expensive to design anindoor anechoic chamber that is the size of a football field. Therefore, the indoor setup shown inFig. 2 is considered as a near-field RCS measurement setup [36]. The illuminating signals emittedby the radar have spherical wavefronts. Therefore, the measured RCS is only an approximationof the true value.In order to accurately measure the RCS of a UAV in an indoor environment, we need tofind a way to generate plane wave illumination (far-field condition) within a short distance.This is achievable in a compact range configuration. The basic principle of a compact rangechamber is to use either an optical lense, parabolic reflector(s), or dielectric lense to collimatethe spherical wavefronts emitted by the radar into a planar wave in a relatively short distance,thus the term “compact range”. Fig. 3 shows different possible compact configurations. However,due to the stringent requirements and cost associated with designing a large perfect collimator,many researchers have not been able investigate this techniques for the RCS measurement ofcommercial UAVs. The next section describes how we use an offset feed compact range anechoicchamber to accurately measure the RCS of commercial UAVs. Test ZoneTx Rx (a) Offset feed Test ZoneTx Rx (b) Cassegrain dual reflector
Test ZoneTx Rx (c) Gregorian dual reflector
Test ZoneRxTx (d) Dual cylindrical reflector
Test ZoneDielectric Lens Tx Rx (e) Dielectric lens reflector Test ZoneRx Tx Load (f) Hologram-based compact rangeFig. 3. Different compact range configurations that could be used for measuring the RCS of a small UAV. Each configurationuses a different approach to collimate the transmitted wave from the radar [40], [41].
IV. UAV RCS M
EASUREMENTS AND C ALIBRATION IN AN O FFSET -F ED C OMPACT -R ANGE A NECHOIC C HAMBER
In this section, we describe our UAV RCS measurement procedure using an offset feedcompact-range anechoic chamber. Fig. 4 is a flowchart that graphically describes the processand techniques employed in this study. As shown in Fig. 4, the first step in measuring the RCSof a target UAV is to capture scattered radar data from the target UAV during a controlledexperiment. The transmit power of the radar is 5 dBm. However, the measured RCS does notdepend on the transmit power or the bandwidth of the radar receiver. Although the bandwidthwill determine the noise floor (noise level) of the radar receiver and thus the signal to noise ratio(SNR) of the received signal, it does not determine the RCS or radar signature of the target.Also, we probe the background with the radar signals to obtain a background response. The Scattered power data from reference Sphere
S(ω) (Frequency)
FrequencyDomain Hann
Windowing
Background power data,
B(ω) (Frequency)Scattered power data from target drone
D(ω) (Frequency) Theoretical RCS of reference sphere ( σ sphere_TH ) (dBsm) D(ω)-B(ω)
S(ω)-B(ω)
Background subtraction
FrequencyDomain Hann
Windowing
IFFT IFFTTime-domain
Target gating (Tukey window) w(n). d(n)
Time-domain
Reference gating (Tukey window) w(n). s(n)
Inaccurate
RCS ( D RCS ) of Drone (Frequency) FFT
Inaccurate
RCS ( S RCS ) of reference (Frequency)
FFT
Calibration
Far field
RCS(σ) of
Drone (dBsm) 𝝈 = 𝝈 𝒔𝐩𝐡𝐞𝐫𝐞_𝐓𝐇 𝑫 𝐑𝐂𝐒 𝑺 𝐑𝐂𝐒
D’ (ɯ)
W (ω) * D’ (ɯ) S’ (ω) * D’ (ɯ) S’ (ɯ)
Fig. 4. Flowchart of the Far-field (plane wave) RCS measurement of the small UAVs in compact range anechoic chamber. scattered data measured from both the target and background are processed and calibrated toobtain the accurate RCS of the target. The measurement setup is described next.
A. Measurement Setup and Procedure
To obtain a plane wave radar illumination within a limited indoor environment, we use the20 foot high collimating parabolic reflector shown in Fig. 5(a). During the measurement, thechamber uses the Keysight E8362B programmable VNA to generate continuous-wave radarsignals, centered at the test frequency. Using a pair of horn antennas, the radar signals are (a) (b)Fig. 5. (a) Large offset feed parabolic reflector, and (b) UAV RCS measurement scenario. transmitted and the backscattered signals from the target UAV are received. The transmit hornantenna (Tx) is connected to Port 1 of the VNA and the receiver antenna (Rx) is connected toPort 2. The VNA measures the scattering transmission coefficient S which is proportional tothe ratio of the reflected (scattered) power at Port 2 to the input power at Port 1. Therefore,using the VNA to implement a radar system, the magnitude of the measured S is proportionalto the RCS of the target UAV in the anechoic chamber [42]. For the 15 GHz RCS measurement,we use the Cobham H-1498 broadband transverse electromagnetic (TEM) horn antennas in theTX and receive (RX) antennas. And for the 25 GHz RCS measurement, we use a Narda 638Standard Gain Horn at both the TX and the RX. These antennas are placed at the offset/focusof the parabolic reflector.The effect of the parabolic reflector is two-fold. First, the reflector changes the curvature ofthe transmitted wave from spherical to planar. The curvature and smoothness of the parabolicreflector ensure that the reflected waves are collimated to simulate far-field conditions at arelatively short distance. Second, from physics, we know that one of the main properties ofradio waves is reflection. By reflection, a surface (a reflector) changes the original direction ofan incoming or incident wave. However, if the reflector is a parabolic surface and the wavesource/feed horn (TX) is located at its focus, then the incident wave from TX is reflected fromthe parabolic surface as plane waves as shown in Fig.3 (a). From Fig. 3(a), we see that thereflected plane waves are now in the direction of the UAV. On reaching the UAV, the planewaves are scattered/reflected once again. The scattered electromagnetic signals are captured by the receiver antenna (RX), which is connected to Port 2 of the VNA. Therefore, the parabolicreflector has performed the dual task of plane wave generation and direction reversal of theincident wave propagating from TX.The scattered signal power ( P scrcv ) is processed to measure the RCS of the UAV. Mathematically,the offset feed compact range is governed by the following expression [43]: P scrcv P o = σλ π ) (cid:18) λR o (cid:19) G T x G Rx = σ · k, (3)where P o is the transmitted power by the feed horn, G f characterizes the gain of the feed hornantennas, R o is the distance from focus (focal point) and the reflector along with the principalray intersection point, and k = λ G Tx G Rx (4 π ) R o is a constant. Therefore, in terms of the scattered andtransmit power, the S measured by the VNA is given in [42] as: S = 10 · log P scrcv P o , (4)From geometry of conic sections, the value of R o can be estimated with respect to the focallength ( f L ) and outside distance ( K ) of the parabolic reflector as [44]: R o = f L + 116 K f L . (5)During the measurement, the UAV is placed on the Styrofoam turntable which is 6 foot awayfrom the antennas, see Fig. 5(b). The turntable, controlled by a stepper motor, rotates the targetthrough the azimuth plane φ ∈ [0 ° , ° ] with a 2° increment. For each look angle, continuouswave signals, centered at the test frequency, are generated in the VNA and transmitted through thetransmit horn antenna (TX). To reduce the effects of unwanted reflections (clutter and multipathreflections) in the chamber, radar absorption materials (RAM) are used. The chamber used inthis study employs pyramidal and wedge-shaped extra high performance (EHP) RAM absorbers.The ETS-Lindgren’s type EHP (Extra High Performance) microwave pyramidal absorbers areused in the front of the feed and the back wall while EHP-18EGCL microwave wedge absorbersare used behind the feed on the side walls, floor, and ceiling. These absorbers reduce multipathreflections from the walls, floor, and ceiling of the anechoic chamber. Typically, the performanceof any RAM absorber depends on its thickness in wavelength [38].After the RCS measurement, the raw data (scattered power in dB) is post-processed to obtainthe accurate RCS of the target UAV in dBsm. Time (ns) -260-240-220-200-180-160-140-120-100-80 M agn i t ude o f S ( d B ) Before Background SubtractionAfter Background Subtraction
TargetreflectionsBack walland MultipathTarget gateTX leakage
Fig. 6. Time domain response of the measurement data showing the effects of background subtraction. The target reflectionscan be isolated from the clutters using a target gate.
B. Post Processing
Post processing is done in MATLAB. Four major post processing operation, shown in heflowchart in Fig. 4, are performed on the captured scattered data. These operations can besummarized as follows. • Step 1: Perform background subtraction on the captured raw data in frequency domain. • Step 2: Band limiting and side lobe reduction using Hann window. • Step 3: Transform the resultant data from frequency to time domain using inverse Fouriertransform (IFFT). • Step 4: Perform time (range) gating on the target zone.The first step in post-processing the raw data obtained during the target measurement isthe background subtraction. The background measurement characterizes the frequency responseof the chamber. To implement background subtraction, we measure the chamber without thetarget UAV mounted on the rotating stand. This measurement is then subtracted from all theUAV RCS measurements (vectorial subtraction). The purpose of background subtraction is toeliminate signals generated by clutters in the environment. Moreover, background subtractionalso helps us to remove unwanted spurious signals such as leakage in the transceiver system andcoupling between the TX and RX antennas. Since all the UAV RCS measurements were carriedout over a wide bandwidth and completed within a short time duration (due to the automation of the measurement process), the background characteristics of the chamber is assumed to beunchanged or very slowly changing during the entire measurement period. Therefore, we do nothave to remeasure the background every time a different UAV is placed on the rotating stand. Itis important to note that background subtraction may not completely remove all the clutter andleakage signals from the measurement data. Therefore, to accurately isolate the intrinsic scatteringdata from the target, we perform time domain transformation using the IFFT operation.After performing the IFFT operation on the resulting data, we obtain the time domain char-acteristics of measurement data. This could be considered as the intrinsic response of the targetin the time domain. Besides, we apply the frequency-domain Hann window before the IFFToperations to band limit the frequency domain data captured by the VNA [45], [46]. This isnecessary to cut-off side high-frequency noise and ripples/side lobes which are present whendata are captured in the frequency domain. Frequency domain ripples tend to asymmetricallyapproach non-zero constants as frequency increases [46]. That is, the high-frequency ripples/noisedo not terminate at zero. As a result, if we perform an IFFT operation, without band-limitingthe spectrum, there will be unwanted time-domain rings. Also, the Hann window is better atband-limiting a frequency spectrum than flattop windows. This is because Hann windows caneasily resolve multiple frequency peaks and by so doing separate the signals of interests fromnoise/ripples/sidelobes [47]. Also, unlike the Hamming window, the endpoints of the Hannwindow smoothly transition to zero making the latter better suitable as a band-limiting filterfor frequency-domain signals.Fig. 6 shows the impulse response of the scattered data. We can see the scattering from thetarget as well as every remaining clutter and leakage. Therefore, to obtain the intrinsic scatteringfrom the target object, we perform time (or range) gating using a windowing function in thetime-domain. This operation is sometimes called software gating [48]. The time-domain softwaregating operation is equivalent to the multiplication of the processed data/signal with a windowingfunction. The Tukey window is suitable for the software gating operation. This is because, incomparison with other time-windowing functions such as the Hann and Hamming windows, thetime-domain Tukey window (tapered cosine function) is less likely to distort the amplitude of thetime-domain transient (time-domain impulse response) which measures the RCS of the target.Therefore, amplitude/FFT gain correction is not necessary when we use a Tukey window in thetime-domain just before an FFT operation. [47].The software gating (or target gating) is used to filter out unwanted time domain responses
12 inches 6 inches 3.75 inches (a)
Frequency (GHz) -80-70-60-50-40-30-20-10 RC S ( d B s m ) BackgroundIdeal 6" sphereMeasured 6" sphereIdeal 3.75" sphereMeasured 3.75" PEC SphereMeasured 12" SphereIdeal12" Sphere (b)Fig. 7. (a) Three standard calibration PEC spheres: 12”, 6”, and 3.75”. The theoretical RCS of each of these spheres can beestimated from their radius, and (b) the ideal and measured RCS (dBsm) of the three standard versus frequency. from the captured signal. That is, signals are accepted or rejected according to the time (range)gates. Signals outside the target time window (target zone) are gated out. This includes multipathand clutter returns from the chamber. The former arises from scatterers that are further awayfrom the target zone while the latter (clutter sources) arises from targets that are located at, ornear the target [38]. The resulting signal is the RCS of the target UAV in time domain. This isconverted into the frequency domain by means of the FFT operation. The resulting frequencydomain RCS data ( D RCS ) is fairly inaccurate. To correct the measurement error, we performcalibrations using standard objects with known RCS.
C. RCS Measurement Calibration
In this study, we use perfectly electrical conducting (PEC) spheres with known theoreticalRCS value for measurement calibration. Besides, due to spherical symmetry, the RCS of thePEC sphere is independent of aspect angle (nonfluctuating or Marcum objects). This makes thePEC sphere a perfect calibration object. Fig. 7(a) shows three standard calibration spheres usedin this experimental study. Only one sphere can be used at a time. However, having measurementfrom multiple PEC calibration spheres allows us to verify the reliability and repeatability of ourcalibration procedure. First, we measure the RCS ( S RCS ) of a PEC calibration sphere in the compact range chamber.Next, we compute the theoretical or exact RCS ( σ T h sphere ) of the calibration sphere. In the far-field,the RCS of a PEC sphere has a closed form analytical expression given by [49] σ T h sphere = λ π (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) ∞ (cid:88) n =1 ( − n (2 n + 1)ˆ H (2) (cid:48) n ( ka ) ˆ H (2) n ( ka ) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) , (6)which can be approximated in two different regions as σ T h sphere ≈ λ π ( ka ) πa (cid:28) λ ( Rayleigh region ) πa a > λ ( Optical region ) , (7)where k = πλ is the wavenumber, a is the radius of the sphere, ˆ H (2) n ( ka ) and ˆ H (2) (cid:48) n are thespherical Hankel function of the second kind of order n and its derivative, respectively.From (6), we can show that the backscattered RCS of a PEC sphere is a function of itscircumference measured in wavelength ( πaλ ). In the Rayleigh region, the size of the PEC sphereis small relative to the wavelength of the signal transmitted by the radar ( πaλ (cid:28) ). On theother hand, in the optical region, the size of the PEC sphere is far larger than the wavelengthof the sphere ( a > λ ). Moreover, between the Rayleigh and the optical regions is the Mie (orresonance) region where the radar wavelength is comparable to the size of the sphere ( πaλ ≈ ).In the Mie region, the RCS of the PEC sphere is dependent on frequency and continuouslyperturbed. However, in the optical region, the RCS of the PEC sphere is a constant that isindependent of frequency. For this reason, we use standard PEC spheres with known theoreticalRCS to calibrate the UAV RCS measurement.Fig. 7(b) shows the measured and theoretical (ideal) RCS of the three PEC spheres consideredin this study. As shown in this figure, the measured RCS varies slightly, while the ideal ortheoretical RCS is a constant. For each calibration sphere, the ratio between the measured ( S RCS )and theoretical RCS ( σ T h sphere ) of the PEC sphere is used to calibrate the measured RCS of thetarget UAV according to: σ UAV = D RCS S RCS · σ T h sphere . (8)After measuring the RCS, the obtained data can be used for further analysis such as UAVRCS statistical modeling and target classification. This will be discussed in the next section.V. RCS S TATISTICAL A NALYSIS AND
UAV C
LASSIFICATION
In this section, we describe the UAV statistical recognition system and the RCS statisticalmodel selection techniques employed in this study. A. RCS-based UAV Classification
Complex radar targets can be modeled as consisting of large numbers of individual scatteringcenters that are randomly distributed. If the individual scatterers are assumed to have the sameRCS, then the echo power from the target object, target RCS returns, can be modeled usingan exponential distribution and ground clutter reflections can be modeled using a Weibulldistribution [50]. Using these statistical models, [3] developed a likelihood ratio test for a singleUAV target detection in the presence of ground clutter interference.However, in practice, many complex radar targets cannot be modeled as an ensemble ofequal-strength scatterers. Besides, for such targets, the radar echo power varies strongly withthe aspect angle, frequency, and polarization of the transmitter and receiver of the radar. Forsuch targets, the best RCS statistical model can only be obtained by empirically fitting themeasured RCS data to a range of possible distributions. This is particularly helpful when wewant to discriminate between multiple targets. That is, if we know the statistical models that bestdescribe different UAV types, we can use this knowledge as the basis for target classification (ortarget discrimination). In such scenarios, the Bayesian-based maximum aposteriori probability(MAP) decision rule is optimal for target classification [51], [52].Given a test RCS data y = ( y , · · · , y n ) that has been recorded from an unknown UAV, itsRCS follows a specific parametric distribution. Suppose, we have M possible UAV classes, thenthe UAV classification problem becomes an M-ary Bayesian hypothesis testing problem, withthe corresponding hypothesis H , H , · · · H M . The likelihood that the test RCS data y belongs tothe z th UAV class (i.e., the likelihood that the H z hypothesis is correct) is given by the posteriorprobability P ( C = z | y ) . According to Bayes theory, P ( C = z | y ) is given by: P ( C = z | y ) = P ( y | C = z ) P ( C = z ) (cid:80) Mk =1 P ( y | C = z ) P ( C = z ) , (9)where P ( C = z ) is the prior probability of the z th class and (cid:80) Mz =1 P ( y | C = z ) P ( C = z ) = P ( y ) is the evidence. Therefore, given the RCS data obtained from an unknown UAV, theRCS-based UAV statistical recognition system determines the class membership of the UAV bycomputing the posterior probabilities of all class membership P ( C = z ) , z = 1 , · · · M . Therefore,the MAP decision rule for the UAV classification problem can be written as: (cid:98) C = arg max C ln P ( C = z | y ) . (10) In practice, since the evidence is not a function of C , it can be ignored. Besides, if we haveequal number of RCS test datasets for each UAV class, then we can assume all the classes areequi-probable. That is, P ( C ) = M , and the decision rule in (10) becomes: (cid:98) C = arg max C ln P ( y | C = z ) . (11)For example, suppose the z th UAV class is described by a gamma distribution model P ( y | C = z ) = P ( y | β, γ ) with scale parameter β and shape parameter γ that can be estimated by fitting the train-ing data to the statistical model of the z th UAV class [53]. The training data σ = ( σ , · · · , σ n ) is obtained from measuring the RCS of the z th UAV in the compact range anechoic chamber asdescribed in Section IV. The model parameters β and γ can be estimated using the maximumlikelihood estimation (MLE) technique. The MLE technique is tractable if we assume thecomponents of the training data σ are independent [51], [52], [54], then the z th UAV classis described by the class model: ln P ( σ | β, γ ) = n (cid:89) i =1 ln P ( σ i | β, γ )= n (cid:88) i =1 ln 1 β γ Γ( γ ) σ γ − i e − σiβ = − nγ ln β − n ln Γ( γ )+( γ − n (cid:88) i =1 ln( n ) − β n (cid:88) i =1 σ i . (12)Using the MLE, we solve the differential equations ∂ ln P ( σ | β,γ ) ∂β = 0 and ∂ ln P ( σ | β,γ ) ∂γ = 0 , andwe obtain ˆ β = ¯ σγ , (13) ln ˆ β + ψ (ˆ γ ) = 1 n n (cid:88) i =1 ln σ i , (14)where ¯ σ is the sample mean of the training data, ˆ β and ˆ γ are the MLE parameter estimate ofthe z th UAV class, and ψ (ˆ γ ) = ∂ln Γ(ˆ γ ) ∂ ˆ γ is the diagamma function. Asymptotically, ψ (ˆ γ ) can beexpanded as a function of either the Riemann zeta function ζ or Bernoulli number B as follows: ψ (ˆ γ ) ≈ ln ˆ γ − γ + ∞ (cid:88) g =1 ζ (1 − g )ˆ γ g , = ln ˆ γ − γ − ∞ (cid:88) g =1 B g g ˆ γ g . (15) (a) (b) (c) (d) (e) (f)Fig. 8. Six small UAVs considered: (a) DJI Matrice 600 Pro, (b) DJI Matrice 100, (c) Trimble zx5, (d) DJI Mavic Pro 1, (e)DJI Inspire 1 Pro, (f) DJI Phantom 4 Pro. Approximating ψ (ˆ γ ) using the first two terms in the expansion given in (15) and substituting(13) in (14) we obtain a quadratic equation whose positive root is ˆ γ . After estimating ˆ β and ˆ γ from the training data σ , we obtain the model P ( σ | ˆ β, ˆ γ ) for the z th UAV. Therefore, given atest RCS data y from an unknown UAV, the log-likelihood that the data is a z th UAV is givenby ln P ( y | ˆ β, ˆ γ ) . Therefore, if we can estimate the statistical model for all the M UAV classes,we can make the UAV classification decision using (11).
B. UAV Statistical Model Selection
While the gamma distribution has been used as an example in the previous subsection tomodel RCS statistics, it may not be the best parametric model for some UAV classes. If/whenthat is the case, the chances of misclassification may increase. Therefore, there is a need toselect the best statistical model for each UAV type using the RCS training data for each UAVclass. Since the true distribution of the RCS of a given UAV class is unknown, we can onlyapproximate it. To do this, we can define a set of candidate statistical models { P ( y | θ ) } anddevelop a statistical criterion for selecting the relatively best statistical model for each UAV typegiven the RCS training (measurement) data.In this study, two statistical model selection techniques will be investigated. The first isthe Akaike information criterion (AIC) and the second is the Bayesian information criterion(BIC) [54]. For any candidate parametric model, the AIC and BIC are respectively computedfrom the training data y = ( y , · · · , y n ) of the z th UAV as:
AIC( y ) = − P ( y | ˆ θ ) + 2 k , (16) BIC( y ) = − P ( y | ˆ θ ) + k ln n , (17) TABLE IIM
EAN , S TD , AND
AIC
SCORE FOR VV - POLARIZED
RCS
DATA . T
HE MODELS ARE
1: L OG - NORMAL , 2: G
ENERALIZEDEXTREME VALUE , 3: G
AMMA , 4: B
ETA , 5: G
ENERALIZED P ARETO , 6: W
EIBULL , 7: N
AKAGAMI , 8: R
AYLEIGH , 9: R
ICIAN ,10: E
XPONENTIAL , 11: N
ORMAL
Freq UAV µ Std AIC Test Score(GHz) (dBsm) (dBsm) 1 2 3 4 5 6 7 8 9 10 1115 DJI Matrice 600 -11.67 1.81 -773.42 -770.55 -773.45 -772.72 -752.08 -758.20 -765.92 -742.09 -753.91 -578.07 -745.81DJI Matrice 100 -14.69 1.69 -1048.24 -1047.22 -1044.92 -1044.22 -996.45 -1021.41 -1032.95 -1002.63 -1017.31 -833.01 -1009.84Trimble zx5 -14.39 2.57 -872.7 -881.88 -842.63 -838.41 -844.95 -817.41 -801.34 -790.48 -788.48 -765.57 -723.83DJI Mavic Pro -17.06 1.51 -1287.91 -1286.23 -1287.48 -1287.33 -1239.65 -1269.53 -1281.23 -1225.12 -1269.71 -1036.63 -1266.59Inspire 1 -14.24 1.56 -1041.35 -1039.38 -1037.39 -1036.68 -1001.06 -1012.32 -1026.45 -981.03 -1011.12 -799.62 -1006.31DJI Phantom 4 Pro -15.02 1.21 -1198.29 -1198.28 -1200.24 -1200.22 -1120.62 -1185.36 -1198.11 -1085.95 -1191.81 -874.72 -1190.9525 DJI Matrice 600 -7.32 2.09 -358.67 -362.48 -363.42 -359.88 -339.62 -351.59 -355.82 -348.23 -347.22 -207.04 -331.25DJI Matrice 100 -11.03 2.27 -637.78 -639.49 -623.88 -617.68 -581.15 -597.57 -594.91 -596.91 -594.91 -504.55 -542.29Trimble zx5 -9.64 2.80 -445.77 -473.69 -392.17 -350.92 -423.31 -367.34 -326.72 -268.9 -266.9 -346.77 -208.26DJI Mavic Pro -16.20 2.30 -1062.91 -1062.93 -1049.06 -1047.52 -1021.02 -1023.99 -1020.80 -1022.74 -1020.74 -933.78 -967.88DJI Inspire 1 -11.09 2.62 -589.96 -603.86 -560.19 -551.33 -595.7 -537.58 -522.88 -510.72 -508.72 -487.83 -447.18DJI Phantom 4 Pro -12.40 1.93 -811.02 -812.43 -796.38 -792.96 -761.76 -764.74 -771.08 -765.48 -763.48 -632.21 -730.08 where θ is the parameter of the model, k is the number of parameters in the statistical model and n is the sample size in the training dataset. We apply the AIC and BIC criteria to the trainingdataset of all the UAVs. The best parametric model for each UAV is stored in the database.In general, the best model is the one with the smaller AIC or BIC score. It is pertinent toselect the RCS statistical models that do not overfit the training data. Overfitting can be achievedby penalizing the complexity of the models. Models with larger k do well in fitting the data;however, there is a trade-off in the increasing variance [54]. For AIC and BIC, the penalty termsare k and k ln n , respectively. Unlike BIC, AIC is asymptotically efficient. On the other hand,BIC is a more consistent estimator since it has a larger penalty term ( k ln n ). The next sectionprovides the results of measurement, statistical model analysis, and classification.VI. M EASUREMENT AND N UMERICAL R ESULTS
In this section, we present the results of the UAV RCS measurements, model selection analysis,and performance analysis of the UAV statistical recognition system. TABLE IIIM
EAN , S TD , AND
BIC
SCORE FOR VV - POLARIZED
RCS
DATA . T
HE MODELS ARE
1: L OG - NORMAL , 2: G
ENERALIZEDEXTREME VALUE , 3: G
AMMA , 4: B
ETA , 5: G
ENERALIZED P ARETO , 6: W
EIBULL , 7: N
AKAGAMI , 8: R
AYLEIGH , 9: R
ICIAN ,10: E
XPONENTIAL , 11: N
ORMAL
Freq UAV µ Std BIC Test Score(GHz) (dBsm) (dBsm) 1 2 3 4 5 6 7 8 9 10 1115 DJI Matrice 600 -11.67 1.81 -767.02 -760.96 -767.05 -766.33 -742.48 -751.81 -759.51 -738.89 -747.52 -574.87 -739.5DJI Matrice 100 -14.69 1.69 -1041.84 -1037.63 -1038.53 -1037.83 -986.85 -1015.01 -1026.55 -999.43 -1010.92 -829.8 -1003.44Trimble zx5 -14.39 2.57 -866.3 -872.29 -836.24 -832.01 -835.36 -811.01 -794.94 -787.28 -782.09 -762.37 -717.43DJI Mavic Pro -17.06 1.51 -1281.51 -1276.63 -1281.08 -1280.94 -1230.05 -1263.13 -1274.83 -1221.92 -1263.31 -1033.43 -1260.19DJI Inspire 1 -14.24 1.56 -1034.95 -1029.78 -1030.99 -1030.28 -991.46 -1005.92 -1020.05 -977.83 -1004.72 -796.42 -999.91DJI Phantom 4 Pro -15.02 1.21 -1191.90 -1188.69 -1193.84 -1193.83 -1111.03 -1178.97 -1191.71 -1082.75 -1185.41 -871.52 -1184.5525 DJI Matrice 600 -7.32 2.09 -352.27 -352.89 -357.02 -353.48 -330.02 -345.19 -349.42 -345.03 -340.82 -203.84 -324.86DJI Matrice 100 -11.03 2.27 -631.38 -629.9 -617.48 -611.28 -571.56 -591.17 -588.52 -593.71 -588.52 -501.36 -535.89Trimble zx5 -9.64 2.80 -439.37 -464.10 -385.77 -344.53 -413.71 -360.94 -320.32 -265.70 -260.50 -343.57 -201.86DJI Mavic Pro -16.20 2.30 -1056.51 -1053.34 -1042.66 -1041.13 -1011.42 -1017.59 -1014.40 -1019.54 -1014.35 -930.58 -961.48DJI Inspire 1 -11.09 2.62 -583.56 -594.26 -553.79 -544.93 -586.10 -531.19 -516.48 -507.52 -502.33 -484.63 -440.78DJI Phantom 4 Pro -12.40 1.93 -804.62 -802.84 -789.98 -786.57 -752.16 -758.34 -764.69 -762.28 -757.08 -629.01 -723.68TABLE IVM
EAN , S TD , AND
AIC
SCORE FOR HH - POLARIZED
RCS
DATA . T
HE MODELS ARE
1: L OG - NORMAL , 2: G
ENERALIZEDEXTREME VALUE , 3: G
AMMA , 4: B
ETA , 5: G
ENERALIZED P ARETO , 6: W
EIBULL , 7: N
AKAGAMI , 8: R
AYLEIGH , 9: R
ICIAN ,10: E
XPONENTIAL , 11: N
ORMAL
Freq UAV µ Std AIC Test Score(GHz) (dBsm) (dBsm) 1 2 3 4 5 6 7 8 9 10 1115 DJI Matrice 600 -12.71 2.33 -768.79 -764.01 -762.55 -761.04 -753.34 -747.13 -747.22 -748.94 -746.94 -644.67 -707.83DJI Matrice 100 -14.73 2.25 -948.58 -948.27 -955.08 -955.36 -949.13 -952.00 -953.29 -950.33 -949.80 -818.86 -932.27Trimble zx5 -14.06 2.61 -838.96 -836.98 -823.41 -819.56 -815.28 -800.96 -788.01 -781.81 -779.81 -740.84 -718.32DJI Mavic Pro -17.29 1.89 -1226.32 -1223.21 -1225.69 -1225.48 -1206.99 -1210.14 -1216.91 -1199.86 -1205.10 -1043.91 -1194.16DJI Inspire 1 -14.43 2.08 -953.04 -951.24 -941.03 -939.26 -928.11 -915.11 -918.18 -917.00 85.00 -915.00 -876.39DJI Phantom 4 Pro -14.87 1.78 -1045.89 -1044.27 -1037.72 -1036.84 -1024.83 -1013.54 -1022.86 -1003.06 -1006.83 -844.72 -995.1725 DJI Matrice 600 -7.07 2.25 -309.72 -305.35 -301.24 -279.44 -304.11 -279.67 -279.61 -281.16 -279.16 -176.40 -235.27DJI Matrice 100 -9.72 1.83 -607.39 -604.04 -605.54 -604.11 -574.07 -590.37 -597.17 -576.1 -584.89 -415.20 -575.73Trimble zx5 -9.69 2.83 -445.56 -444.75 -425.68 -411.95 -413.99 -407.86 -392.48 -374.65 -372.65 -363.97 -315.90DJI Mavic Pro -17.22 2.68 -1092.89 -1115.53 -1115.95 -1116.46 -1101.2884 -1120.76 -1120.81 -1122.62 -1120.64 -1013.82 -1101.63DJI Inspire 1 -12.05 3.42 -574.30 -587.87 -535.46 -525.55 -574.49 -524.39 -494.05 -403.44 -401.44 -516.17 -374.14DJI Phantom 4 Pro -12.24 1.69 -845.30 -845.08 -836.12 -834.46 -823.96 -810.64 -821.65 -794.43 -804.60 -628.07 -795.78 TABLE VM
EAN , S TD , AND
BIC
SCORE FOR HH - POLARIZED
RCS
DATA . T
HE MODELS ARE
1: L OG - NORMAL , 2: G
ENERALIZEDEXTREME VALUE , 3: G
AMMA , 4: B
ETA , 5: G
ENERALIZED P ARETO , 6: W
EIBULL , 7: N
AKAGAMI , 8: R
AYLEIGH , 9: R
ICIAN ,10: E
XPONENTIAL , 11: N
ORMAL
Freq UAV µ Std BIC Test Score(GHz) (dBsm) (dBsm) 1 2 3 4 5 6 7 8 9 10 1115 DJI Matrice 600 -12.71 2.33 -762.39 -754.4 -756.15 -754.64 -743.75 -740.74 -740.82 -745.74 -740.54 -641.47 -701.43DJI Matrice 100 -14.73 2.25 -942.19 -938.68 -948.68 -948.96 -939.53 -945.60 -946.89 -947.13 -943.41 -815.66 -925.87Trimble zx5 -14.06 2.61 -832.56 -827.38 -817.02 -813.16 -805.68 -794.56 -781.6 -778.61 -773.41 -737.64 -711.92DJI Mavic Pro -17.29 1.89 -1219.92 -1213.61 -1219.29 -1219.09 -1197.39 -1203.75 -1210.52 -1196.66 -1198.70 -140.71 -1187.77DJI Inspire 1 -14.43 2.08 -946.64 -941.65 -934.63 -932.87 -918.51 -908.71 -911.78 -911.78 -908.60 -793.20 -870.00DJI Phantom 4 Pro -14.87 1.78 -1039.50 -1034.68 -1031.32 -1030.44 -1015.24 -1007.14 -1016.46 -999.86 -1000.43 -841.52 -988.7825 DJI Matrice 600 -7.07 2.25 -303.33 -295.76 -294.84 -273.05 -294.51 -273.27 -273.21 -277.97 -272.77 -173.20 -228.87DJI Matrice 100 -9.72 1.83 -600.99 -594.44 -599.15 -597.72 -564.47 -583.97 -590.78 -572.90 -578.49 -412.01 -569.34Trimble zx5 -9.69 2.83 -439.16 -435.15 -419.28 -405.55 -404.39 -401.47 -386.08 -371.45 -366.26 -360.77 -309.5DJI Mavic Pro -17.22 2.68 -1086.49 -1105.94 -1109.55 -1110.07 -1091.69 -1114.37 -1114.42 -1119.42 -1114.24 -1010.62 -1095.23DJI Inspire 1 -12.05 3.42 -567.91 -578.28 -529.06 -519.16 -564.89 -518.00 -487.65 -400.24 -395.04 -512.97 -367.74DJI Phantom 4 Pro -12.24 1.69 -838.9 -835.49 -829.73 -828.07 -814.36 -804.25 -815.26 -791.23 -798.21 -624.87 -789.38
A. RCS Measurement Results
In this section, we present the RCS measurement results of the six UAVs shown in Fig. 8.For each UAV, the complex transmission coefficient S is measured in the frequency range14.5-15.5 GHz and 24.5-25.5 GHz in steps of 5 MHz. This gives 201 frequency points and themeasured S data file has a length of 72762 ×
1. The S data file can be reshaped to an array201 × × φ ∈ [0 ° , ° ] with a 2° increment). Therefore, for a specific frequency pointand polarization, the measured S has a length of 181 ×
1. After post-processing and calibration,the RCS of the UAVs is estimated from S as described in Section III-B. The measured RCSdata constitute the training dataset. The database contains the best-fitting statistical model foreach UAV class estimated from the training dataset by either the AIC or BIC criteria as describedin Section V-B.Due to the low reflective materials used in the UAV design, the average RCS values are lessthan dBsm. For the 15 GHz VV-polarization measurement, the average RCS of DJI Matrice600, DJI Matrice 100, Trimble zx5, DJI Mavic Pro, DJI Inspire 1, and DJI Phantom 4 Pro are − . dBsm, − . dBsm, − . dBsm, − . dBsm, − . dBsm, and − . dBsm, ° ° ° ° ° ° ° ° ° ° ° ° ° -165 ° -150 ° -135 ° -120 ° -105 ° -90 ° -75 ° -60 ° -45 ° -30 ° -15 ° -20-15-10-50 HH 15 GHzHH 25 GHzVV 15 GHzVV 25 GHz (a) ° ° ° ° ° ° ° ° ° ° ° ° ° -165 ° -150 ° -135 ° -120 ° -105 ° -90 ° -75 ° -60 ° -45 ° -30 ° -15 ° -20-15-10-5 HH 15 GHzHH 25 GHzVV 15 GHzVV 25 GHz (b) ° ° ° ° ° ° ° ° ° ° ° ° ° -165 ° -150 ° -135 ° -120 ° -105 ° -90 ° -75 ° -60 ° -45 ° -30 ° -15 ° -20-15-10-50 HH 15 GHzHH 25 GHzVV 15 GHzVV 25 GHz (c) ° ° ° ° ° ° ° ° ° ° ° ° ° -165 ° -150 ° -135 ° -120 ° -105 ° -90 ° -75 ° -60 ° -45 ° -30 ° -15 ° -20-15-10 HH 15 GHzHH 25 GHzVV 15 GHzVV 25 GHz (d) ° ° ° ° ° ° ° ° ° ° ° ° ° -165 ° -150 ° -135 ° -120 ° -105 ° -90 ° -75 ° -60 ° -45 ° -30 ° -15 ° -20-15-10-50 HH 15 GHzHH 25 GHzVV 15 GHzVV 25 GHz (e) ° ° ° ° ° ° ° ° ° ° ° ° ° -165 ° -150 ° -135 ° -120 ° -105 ° -90 ° -75 ° -60 ° -45 ° -30 ° -15 ° -20-15-10-5 HH 15GHzHH 25GHzVV 15GHzVV 25GHz (f)Fig. 9. The measured RCS (dBsm) versus azimuth angles ( φ ∈ [0 ° , ° ] ) for the small UAVs: (a) DJI Matrice 600 Pro, (b)DJI Matrice 100, (c) Trimble zx5, (d) DJI Mavic Pro 1, (e) DJI Inspire 1 Pro, (f) DJI Phantom 4 Pro. respectively. For the same UAV set, the average VV-polarized RCS, measured at 25 GHz are − . dBsm, − . dBsm, − . dBsm, − . dBsm, − . dBsm, and − . dBsm,respectively. Tables II-V provide a summary of the mean and the standard deviation (Std) of theRCS for all the cases considered. From these values, we observe that for each of the UAVs, theaverage VV polarized RCS measured at 25 GHz is greater than the value obtained at 15 GHz.This observation is also true about the average HH-polarized RCS values. This is probably dueto the diffraction effects of sharp corners at higher frequencies. Consequently, higher frequencyradars are more suitable for ATR and KB radar systems, especially when the target of interestis a small UAV.Furthermore, from Tables II-V, we observe that the two bigger UAVs, DJI Matrice 600 andTrimble zx5, have relatively higher average RCS. This is probably because the arms and framesof these UAVs are designed with carbon fiber which can support the weight of large batteries andpayload requirements of large UAVs. It is well known that carbon fiber has a higher reflectivitythan plastics which is used in the design of the smaller UAVs. Moreover, the measured RCS depends on other factors as well. This observation is depicted by the RCS signature of the sixUAVs which is shown in Fig. 9. The RCS signature is a polar plot of the RCS (dBsm), measuredat a specific frequency and polarization, versus azimuth angle. From Fig. 9, we see that the RCSof each UAV is dependent on the aspect angle, frequency, polarization, and shape of the UAV.For instance, from Fig. 9, we can recognize some of the physical features (shape) of the UAVs.From these signatures, we can recognize the dominant scattering areas around the arms andthe front frame of each UAV. Therefore, through the radar or RCS signatures, UAVs could bedistinguished from other airborne objects like manned-aircraft, missiles, and birds. Besides, usingthe RCS signature we could discriminate between different commercial UAV types by utilizinga statistical recognition system. Moreover, from Fig. 9, we see that the VV and HH-polarizedsignature are a little different for each UAV. B. Results of RCS Model Selection Analysis
In this section, the results of model selection for the measured UAV RCS are presented. Inthis study, 11 different candidate statistical models will be investigated for all six UAV types.The statistical models are lognormal, generalized extreme value (GEV), gamma, beta, generalizedPareto (GP), Weibull, Nakagami, Rayleigh, Rician, exponential, and normal statistics. The datasetconsists of UAV RCS measurement at 15 GHz and 25 GHz in both the VV-and HH polarization.For each of the UAVs, Table II and Table III present the AIC and BIC test scores, respectivelyusing the VV-polarized RCS measurement data. On the other hand, Table IV and Table V presentthe AIC and BIC test scores, respectively using the HH-polarized RCS measurement data. Foreach UAV type, the best RCS model is selected as the model with the lowest AIC or BIC testscore. In the tables, the best model for each UAV is represented by the highlighted cell. From thetables, we observe that except for the 25 GHz VV-polarized RCS data, both the AIC and BICcriteria select the same statistical model as the best. Furthermore, we observe that the lognormalis the most frequently selected statistical model for the UAV RCS measurement data. This isfollowed by the GEV and gamma statistical models. Interestingly, in [36], the authors claimedthe Gaussian statistics is a good model for the UAV RCS data for measurements at mmWavefrequencies. However, our studies have shown there are better statistical models, at least basedon our measurements at 15 GHz and 25 GHz.To better describe the relative performance of all the 11 statistical models, we can analyzetheir probability distributions. Fig. 10 provides a plot of the probability distribution of each RCS (dBsm)
0 0.20.40.60.8 P r obab ili t y D en s i t y EmpiricalGammaLognormalBetaGEVNakagami (a) DJI Matrice 600: VV
RCS (dBsm)
0 0.20.40.60.81 P r obab ili t y D en s i t y EmpiricalLognormalGEVGammaBetaGP (b) DJI Matrice 600: HH
RCS (dBsm)
0 0.10.20.30.40.50.60.70.80.91 P r obab ili t y D en s i t y EmpiricalLognormalGEVGammaBetaNakagami (c) DJI Matrice 100: VV
RCS (dBsm)
0 0.110.220.330.440.560.670.780.891 P r obab ili t y D en s i t y EmpiricalBetaGammaNakagamiWeibullRayleigh (d) DJI Matrice 100: HH
RCS (dBsm)
0 0.130.250.380.5 0.630.750.881 P r obab ili t y D en s i t y EmpiricalGEVLognormalGPGammaBeta (e) Trimble zx5: VV
RCS (dBsm)
0 0.170.330.5 0.670.831 P r obab ili t y D en s i t y EmpiricalLognormalGEVGammaBetaGP (f) Trimble zx5: HH
RCS (dBsm)
0 0.170.330.5 0.670.831 P r obab ili t y D en s i t y EmpiricalLognormalGammaBetaGEVNakagami (g) DJI Mavic Pro: VV
RCS (dBsm)
0 0.140.290.430.570.710.861 P r obab ili t y D en s i t y EmpiricalLognormalGammaBetaGEVNakagami (h) DJI Mavic Pro: HH
RCS (dBsm)
0 0.10.20.30.40.50.60.70.80.91 P r obab ili t y D en s i t y EmpiricalLognormalGEVGammaBetaNakagami (i) DJI Inspire 1: VV
RCS (dBsm)
0 0.140.290.430.570.710.861 P r obab ili t y D en s i t y EmpiricalLognormalGEVGammaBetaGP (j) DJI Inspire 1: HH
RCS (dBsm)
0 0.130.250.380.5 0.630.750.881 P r obab ili t y D en s i t y EmpiricalGammaBetaLognormalGEVNakagami (k) DJI Phantom 4 Pro: VV
RCS (dBsm)
0 0.10.20.30.40.50.60.70.80.91 P r obab ili t y D en s i t y EmpiricalLognormalGEVGammaBetaGP (l) DJI Phantom 4 Pro: HHFig. 10. The probability distribution of the best five statistical models fitted to the UAV RCS data measured at 15 GHz (VV andHH-polarization). The histogram is the empirical statistics of the measured data which is fitted to different statistical distributions.The plot legends show in decreasing order (moving down) the relative fit of the statistical models according to the AIC criterion. of the statistical models given the UAV RCS data measured at 15 GHz. From the probabilitydistribution plots, we can verify that both lognormal and GEV models are relatively better infitting the experimental or empirical RCS data of all six commercial UAVs measured at 15 GHz.This is probably because lognormal and GEV distributions are heavy-tailed and could well fitthe extremities of the skewed measurement data. On the contrary, the Gaussian distribution is often suitable for symmetric data. However, from the histograms in Fig. 10, we see that theempirical data is not symmetric. Besides, for each UAV type, the parameters of the statisticalmodels will vary depending on the radar system parameters such as frequency and polarization.Thus, for a given radar system, knowing the most appropriate RCS statistics of a specific UAVtype could help discriminate/classify the UAV from other objects. The results of statistical-basedUAV recognition/classification will be discussed next. C. Analysis of UAV Statistical Recognition System Using all Azimuth RCS Data
In this subsection, we describe the results of the UAV recognition/classification at differentSNR using all azimuth RCS data from each of the UAV (( φ ∈ [0 ◦ , ◦ ) with a 2 ◦ increment).First, we need to estimate the Gaussian noise power ( σ N ) for the different SNR considered inthe analysis. For instance, given a specific SNR and the time-domain radar response (scattereddata) a k ( t ) from an unknown k -th UAV, the noise power σ is estimated as: σ N = P k − SNR / , (18)where P k = 1 T (cid:90) T a k ( t ) d t = (cid:80) Ni =1 (cid:12)(cid:12) √ σ VV (cid:12)(cid:12) N , VV-polarization (cid:80) Ni =1 (cid:12)(cid:12) √ σ HH (cid:12)(cid:12) N , HH-polarization (19)is the average power of the time domain return a k ( t ) from the unknown UAV, T is the responseinterval, and N is the number of discrete samples of the frequency domain RCS data. Theoutcome in (19) is a consequence of the Parseval’s theorem.Once σ has been estimated, we can add the appropriate noise signal to the test signals andperform classification. To evaluate the performance of the UAV recognition system, we generatea test dataset by running the Monte Carlo simulation over a range of SNRs. For each SNR, 500noisy RCS test data are generated by adding appropriate Gaussian noise to the measurementdata. The test data are used for classification. The test samples are passed through the statisticalrecognition system which computes the likelihood that each of the test data is a member of oneof the UAV classes in the database.Fig. 11 shows the average classification accuracy versus SNR at different frequencies andpolarizations. Also, Fig. 11 highlights the performance of the different model selection criteriaused for the training database. We see that the average UAV classification accuracy is the samein the case of the 15 GHz VV-polarized test data, irrespective of which criteria was used for
0 2 4 6 8 10 12 14
SNR (dB) A v e r age c l a ss i f i c a t i on a cc u r a cy ( % ) VV - 15 GHz; AIC/BICVV - 25 GHz; AICVV - 25 GHz; BICHH - 15 GHz; AIC/BICHH - 25 GHz; AIC/BIC
Fig. 11. Average classification vs SNR for six drones evaluated at 15 GHz and 25 GHz measured using both the VV andHH-polarized RCS data. This result is based on all the azimuth RCS data from each of the UAV (( φ ∈ [0 ◦ , ◦ ) with a 2 ◦ increment) selecting the best statistical models for the UAV in the database. A similar observation can beseen in the case of the 15 GHz and 25 GHz HH-polarized test data. To explain this observation,we look at Tables II-V. From these tables, we see that both AIC and BIC selects the samestatistical models for the database. Therefore, the classification results are similar in these cases.On the contrary, for the 25 GHz VV-polarized test data, AIC and BIC criteria select a differentstatistical model for some of the UAVs in the database. Therefore, the classification accuracyslightly differs as shown in Fig. 11.Also, from Fig. 11, we see that the UAV classification accuracy increases with SNR. For the15 GHz and 25 GHz VV-polarized RCS test data, the average classification accuracy is 49.67%and 49.33% at 0 dB SNR and 99.17% and 99.53% at 10 dB SNR. Similarly, for the 15 GHzand 25 GHz HH-polarized RCS test data, the average classification accuracy is 47.63% and35.53% at 0 dB SNR and 97.43% and 100% at 10 dB SNR. Besides, Fig. 11 also shows thatat SNR below 3 dB, the classification accuracy for the HH-polarized RCS test data is relativelylower than the VV-polarized RCS test data. This is probably because AIC and BIC mostly selectthe same statistical model (lognormal) for all the HH-polarized UAV RCS data in the database. -4.5 -4 -3.5 -3 -2.5 Log location
Log sc a l e DJI Matrice 600DJI Inspire 1DJI Mavic ProDJI Phantom 4 ProTrimble zx5 (a) -4.5 -4 -3.5 -3 -2.5
Log location
Log sc a l e DJI Matrice 600DJI Inspire 1DJI Mavic ProDJI Phantom 4 ProTrimble zx5 (b)Fig. 12. Scatter plots for parameters of the lognormal statistical model fitted to the 15 GHz HH polarized RCS test data at: (a)0 dB SNR, (b) 10 dB SNR.
Even if each UAV type in the database is described by a unique lognormal statistics, havingthe same model type for the different UAVs could lead to some confusion at low SNR. This isbecause at low SNR, the additive Gaussian noise cause the parameter values of the lognormalstatistical models of the HH-polarized RCS test data to come closer together which can lead toconfusion in the UAV classification. This observation is depicted by the scatter plots shown inFig. 12. In Fig. 12(a), we see a significant overlap between the lognormal parameters of DJIInspire 1 and Trimble zx5 on one hand, and between DJI Inspire 1 and DJI Phantom 4 Pro onthe other hand. Also, there is a little overlap, between the parameters of the DJI Matrice 600and Trimble zx5. The overlapping of the lognormal parameter at of 0 dB SNR will affect theclassification accuracy of the UAV statistical recognition system. However, at an SNR of 10 dB,Fig. 12(b) shows a reduced overlap between the lognormal parameters. Therefore, we wouldexpect a higher recognition rate as SNR increases.To further analyze the classification performance of the UAV statistical recognition system,we generate the confusion matrices for the UAV statistical recognition system using the VVand HH-polarized test data and AIC model selection criterion for the database. The confusionmatrix gives us an idea of what the UAV recognition system is getting right and what kind ofmisclassification occurs. In the confusion matrix, the diagonal elements represent the instancesof correct classification while the off-diagonal elements represent the misclassifications. Fig. 13shows the confusion matrices generated at 10 dB SNR by averaging the results of the MonteCarlo simulation. For the 15 GHz and 25 GHz VV-polarized RCS test data, the DJI Matrice 100 D J I M a t r i c e D J I M a t r i c e D J I I n s p i r e D J I M a v i c P r o D J I P han t o m P r o T r i m b l e zx Target class D J I M a t r i c e D J I M a t r i c e D J I I n s p i r e D J I M a v i c P r o D J I P han t o m P r o T r i m b l e zx O u t pu t c l a ss (a) VV 15 GHz, AIC D J I M a t r i c e D J I M a t r i c e D J I I n s p i r e D J I M a v i c P r o D J I P han t o m P r o T r i m b l e zx Target class D J I M a t r i c e D J I M a t r i c e D J I I n s p i r e D J I M a v i c P r o D J I P han t o m P r o T r i m b l e zx O u t pu t c l a ss (b) VV 25 GHz, AIC D J I M a t r i c e D J I M a t r i c e D J I I n s p i r e D J I M a v i c P r o D J I P han t o m P r o T r i m b l e zx Target class D J I M a t r i c e D J I M a t r i c e D J I I n s p i r e D J I M a v i c P r o D J I P han t o m P r o T r i m b l e zx O u t pu t c l a ss (c) HH 15 GHz, AIC D J I M a t r i c e D J I M a t r i c e D J I I n s p i r e D J I M a v i c P r o D J I P han t o m P r o T r i m b l e zx Target class D J I M a t r i c e D J I M a t r i c e D J I I n s p i r e D J I M a v i c P r o D J I P han t o m P r o T r i m b l e zx O u t pu t c l a ss (d) HH 25 GHz, AICFig. 13. The confusion matrices of the UAV statistical recognition system at 10 dB SNR. These matrices are obtained whenwe use the AIC criterion for the database. In each matrix, the degree of confusion is specified by the colorbar in terms of theprobability of confusion ρ . Moving down the colorbar, the value of ρ increases, signifying increasing confusion. is sometimes confused (misclassified) as the DJI Inspire 1 and vice-versa. This accounts for allthe misclassification when we use the VV-polarized RCS test data to perform UAV statisticalrecognition. On the other hand, using the 15 GHz HH-polarized RCS test data, there are severalinstances of misclassification between DJI Matrice 100, DJI Inspire 1, Trimble zx5, and Phantom4 Pro UAVs. However, the percentage of the misclassification (sum of the off-diagonal rates)is not significant at 10 dB. This observation is consistent with the scatter plot in Fig. 12(b).For instance, using the 15 GHz HH-polarized, only 0.4% of the DJI Matrice 100 test data aremisclassified as either Trimble Zx5 or DJI Phantom 4 Pro; only 0.8% of the DJI Inspire 1 testdata are misclassified as Trimble zx5; only 0.8% of DJI Phantom 4 Pro are misclassified as DJI
0 2 4 6 8 10 12 14 16 18 20 22 24
SNR (dB) A v e r age c l a ss i f i c a t i on a cc u r a cy ( % )
15 GHz: HH, AIC15 GHz: VV, AIC25 GHz: HH, AIC25 GHz: VV, AIC
Fig. 14. The average classification of the six drones in the case where the radar sees only 120 ◦ sector RCS reflections fromthe approaching targets. The classification is evaluated at 15 GHz and 25 GHz measured using both the VV and HH-polarizedRCS data. Matrice 100. Besides, the percentage of correct classification (average of all diagonal elements)is about 97.43%. Furthermore, Fig. 13 shows that there are no misclassifications for the 25GHz HH-polarized RCS test data at 10 dB SNR. Therefore, for improved UAV recognition, wesuggest the use of the 25 GHz HH-polarized RCS test data and the lognormal statistics for thedatabase.
D. Analysis of UAV Statistical Recognition System Using Limited Azimuth RCS Data
In Section VI-C, we evaluated the performance of the UAV statistical recognition systemusing the RCS data measured from all around the UAVs (( φ ∈ [0 ◦ , ◦ ) with a 2 ◦ increment).However, in many instances, the field of view (FOV) is limited. That is, the radar only sees asector of the approaching target. For instance, some practical radars, like the Fortem radar [6],can only detect an incoming UAV within a 120 ◦ sector. In that case, UAV recognition system hasto make a classification using the radar reflection data (RCS) captured from within the limitedFOV of the radar. Fig. 14 shows the average classification of the six drones when the FOV of D J I M a t r i ce Target class D J I M . D J I I n s p i r e D J I M av i c P r o D J I P h a n t o m D J I T r i m b l e O u t pu t c l ass (a) D J I M av i c P r o Target class D J I M D J I M D J I I n s p i r e D J I P h a n t o m D J I T r i m b l e O u t pu t c l ass (b)Fig. 15. Classifying UAVs of the same family at 14 dB SNR and 25 GHz HH : (a) DJI Matrice 600 classified as Trimble zx5,and (b) DJI Mavic Pro classified as DJI Phantom 4 Pro. the radar is 120 ◦ (centered around 0 ◦ or ( φ ∈ [ − ◦ , ◦ ] with a 2 ◦ increment) in the azimuthplane. In this case, we observe the average classification accuracy is relatively smaller than whatis reported in Fig. 11. At 14 dB SNR, Fig. 14 shows that the classification algorithm achievesan accuracy of 80.4%, 92.1667%, 84.2%, and 83.2% for 15 GHz HH, 15 GHz VV, 25 GHzHH, and 25 GHz VV respectively. In comparison, at 14 dB, Fig. 11 shows that the classificationalgorithm achieves 97.5%, 99.07%, 100%, and 100% for 15 GHz HH, 15 GHz VV, 25 GHzHH, and 25 GHz VV respectively. However, Fig. 14 shows that as SNR increases, the averageclassification accuracy gets better even with limited azimuth angles. In general, the wider theazimuth beamwidth of the radar and the higher the SNR, the better the performance of the UAVstatistical recognition system. E. Classifying an Unknown UAV from the Same Family as One of the UAVs in the Database
In this subsection, we are interested in investigating the performance of the UAV statisticalrecognition system when an unknown UAV is observed by the radar. Suppose the shape/materialproperties of the unknown UAV is similar to one of the UAVs in the database, then for thepurpose of this experiment, we will assume both belong to the same family. Therefore, we areinterested in knowing if the UAV statistical recognition system will identify the similarity in thedatabase and appropriately classify the unknown UAV. For example, by observing the UAVs in -5 0 5 SNR (dB) A v e r age c l a ss i f i c a t i on a cc u r a cy ( % ) DJI Matrice 600 --> Trimble zx5DJI Mavic Pro --> Phantom 4 Pro
Fig. 16. Average classification accuracy versus SNR for the unknown UAV classification experiment. In this experiment, theunknown UAV is similar to one of the UAVs in the database
Fig. 8, we notice that two pairs of UAVs look alike. The first pair of UAVs is DJI Matrice 600Pro and Trimble zx5. The second pair of UAVs is DJI Mavic Pro and DJI Phantom 4 Pro.To perform this classification experiment, we train the UAV statistical recognition systemwith five drones instead of six. Then, we take the sixth UAV (which is excluded from thetraining database) and use it for classification. For example, we use the unknown UAV as theDJI Matrice 600, which belongs to the same family as the Trimble zx5 UAV in our trainingdatabase. To perform a classification experiment, we run a Monte Carlo simulation with the 100DJI Matrice 600 RCS test data, average the classification results, and then plot the confusionmatrix at 14 dB SNR. The result is shown in Fig. 15(a). We noticed all 100 RCS test data ofDJI Mavic Pro are classified as the Trimble zx5 drone. We performed a similar experiment, thistime our database includes DJI Matrice 600 but excludes DJI Mavic Pro (the unknown UAV).We performed classification using a similar Monte Carlo analysis. Fig. 15(b) shows that all 100DJI Mavic Pro test data are classified as DJI Phantom 4 Pro at 14 dB SNR. Fig. 16 shows theresult of classifying the unknown UAVs versus SNR. Form Fig. 16, we see that even at 5 dBSNR, the UAV statistical recognition system achieves an accuracy of 100 % when classifyingthe unknown UAV into the appropriate family in the training database. However, as the SNR reduces below 3 dB, the average classification accuracy falls sharply. Therefore, we concludethat the UAV statistical recognition system can identify the similarity between the RCS statisticsof an unknown UAV and a known UAV in the training database.On the contrary, if the unknown UAV or radar target is not similar to any of the classesor family in the database, then any attempt to classify the object would yield an error. Thisis a fundamental limitation of all supervised learning systems (statistical and machine learningalgorithms). However, several studies have proposed the use of a “rejection algorithm” [55]–[57]when classifying an unknown target or object. A rejection algorithm basically would prevent anyattempt to classify an unknown target if the target statistics are not similar or close to the knownclasses/families in the training database. However, to measure similarity or closeness, a rejectionalgorithm has to estimate a rejection threshold, which is a non-trivial task. Often times, thereis no closed-form analytical expression to use when estimating the rejection threshold. One hasto try classifying all possible “unknown object” and use that information to decide the value ofthe rejection threshold. This is an exhaustive process since there is no end to the list of possibleunknown objects that could confuse a supervised learning system. Besides, the design of sucha rejection algorithm is beyond the scope of the current study.VII. C ONCLUSION
The paper presented a detailed experimental procedure for accurately measuring the RCS ofcommercial UAVs in a compact range anechoic chamber at 15 GHz and 25 GHz in both VV andHH polarization. The paper describes how the target UAVs can be modeled by fitting their RCSdata to a set of 11 statistical models whose parameters are estimated using maximum likelihoodtechniques. The best statistical model that represents a given UAV type is selected with the aidof AIC and BIC model selection criteria. From the model selection analysis, we observe thatthe lognormal and GEV distributions are very good at modeling the RCS of the commercialUAVs. This is probably because the data are heavy-tailed and skewed. We also observe that theGaussian statistics did not perform so well since the radar target returns from the UAVs are notsymmetric. Using the best statistical model for each UAV type in the database, we propose a UAVstatistical recognition system whose performance is evaluated at different SNRs. We provided theaverage classification plot which shows that at 10 dB, an average accuracy of 97.43% or more isachievable. Also, the confusion matrices are provided to analyze the strength and weaknesses ofthe recognition system. The confusion matrices show that at 10 dB SNR, the HH-polarized RCS data is best for identifying the UAVs. Furthermore, we evaluated the performance of the UAVstatistical recognition system in a scenario where the radar can only capture limited RCS aspectreflections from the target object. We showed that at high SNR, the UAV statistical recognitionsystem still achieves good average classification accuracy. Also, we evaluated the performanceof the UAV statistical recognition system when an unknown UAV, similar to one of the UAVsin the training database, is to be classified.In the future, we are planning to extend our work to include statistical recognition of UAVsusing inverse synthetic aperture radar (ISAR) image data. The ISAR image is a 2-dimensionalradar imaging technique that can provide rich spatial features for target recognition. Moreover, toenhance UAV recognition rates in narrow field of view (FOV) scenarios, we plan to explore waysto harness features from both ISAR images and micro-Doppler signature. Fusing multi-domainradar statistical features could greatly improve UAV recognition, especially at far distances. Also,we are interested in investigating the use of mixture statistical models for UAV RCS modeling,which could provide better UAV classification at low SNR scenarios.A CKNOWLEDGMENT
The authors would like to thank Mr. Kenneth Ayotte and the management of the Ohio StateUniversity Electroscience Laboratory for their help with the RCS measurements.R
EFERENCES [1] B. A. Card, “Terror from above: How the commercial unmanned aerial vehicle revolution threatens the US threshold,”
Air& Space Power Journal , vol. 32, no. 1, pp. 80–96, Mar. 2018.[2] I. Guvenc, F. Koohifar, S. Singh, M. L. Sichitiu, and D. Matolak, “Detection, tracking, and interdiction for amateur drones,”
IEEE Commun. Mag. , vol. 56, no. 4, pp. 75–81, Apr. 2018.[3] M. Ezuma, O. Ozdemir, C. Kumar, W. A. Gulzar, and I. Guvenc, “Micro-UAV detection with a low-grazing angle millimeterwave radar,” in
Proc. IEEE Radio Wireless Symp. (RWS) Conf.,Orlando, FL , Jan. 2019, pp. 1–4.[4] M. Ezuma, F. Erden, C. K. Anjinappa, O. Ozdemir, and I. Guvenc, “Detection and classification of UAVs using RFfingerprints in the presence of Wi-Fi and Bluetooth interference,”
IEEE OJ-COMS , vol. 1, pp. 60–76, Nov. 2019.[5] F. Gini and M. Rangaswamy,
Knowledge based radar detection, tracking and classification . Hoboken, NJ: John Wiley& Sons, May 2008.[6] [Online]. Available: https://fortemtech.com/[7] [Online]. Available: https://ancortek.com/wp-content/uploads/2020/05/SDR-2400AD2-Datasheet.pdf[8] A. Lauˇcys, S. Rudys, M. Kinka, P. Ragulis, J. Aleksandraviˇcius, D. Jablonskas, D. Bruˇcas, E. Daug˙ela, and L. Maˇciulis,“Investigation of detection possibility of UAVs using low cost marine radar,”
Aviation , vol. 23, no. 2, pp. 48–53, May2019. [9] R. Guay, G. Drolet, and J. R. Bray, “Measurement and modelling of the dynamic radar cross-section of an unmannedaerial vehicle,” IET Radar, Sonar & Navigation , vol. 11, no. 7, pp. 1155–1160, July 2017.[10] M. Ezuma, M. Funderburk, and I. Guvenc, “Compact-range RCS measurements and modeling of small drones at 15 GHzand 25 GHz,” in
Proc. IEEE Radio and Wireless Symp. (RWS) Conf. , San Antonio, TX, Mar. 2020, pp. 313–316.[11] S. Rahman and D. A. Robertson, “Classification of drones and birds using convolutional neural networks applied to radarmicro-doppler spectrogram images,”
IET Radar Sonar Nav. , vol. 14, no. 5, pp. 653–661, Mar. 2020.[12] ——, “Radar micro-doppler signatures of drones and birds at K-band and W-band,”
Scientific Reports , vol. 8, no. 1, pp.1–11, Nov. 2018.[13] M. Ritchie, F. Fioranelli, H. Borrion, and H. Griffiths, “Multistatic micro-doppler radar feature extraction for classificationof unloaded/loaded micro-drones,”
IET Radar Sonar Nav. , vol. 11, no. 1, pp. 116–124, Apr. 2016.[14] S.-J. Lee, S.-J. Jeong, B.-S. Kang, H. Kim, S.-M. Chon, H.-G. Na, and K.-T. Kim, “Classification of shell-shaped targetsusing RCS and fuzzy classifier,”
IEEE Trans. Antennas Propag. , vol. 64, no. 4, pp. 1434–1443, Apr. 2016.[15] V. C. Chen,
The micro-Doppler effect in radar . Norwood, MA: Artech House, Feb. 2019.[16] P. Klaer, A. Huang, P. S´evigny, S. Rajan, S. Pant, P. Patnaik, and B. Balaji, “An investigation of rotary drone HERM linespectrum under manoeuvering conditions,”
Sensors , vol. 20, no. 20, pp. 1–15, Jan. 2020.[17] V. C. Chen,
Inverse Synthetic Aperture Radar Imaging; Principles . Edison, NJ: Institution of Engineering and Technology,Sept. 2014.[18] C. J. Li and H. Ling, “An investigation on the radar signatures of small consumer drones,”
IEEE Antennas Wirel. Propag.Lett. , vol. 16, pp. 649–652, July 2016.[19] M. Pieraccini, L. Miccinesi, and N. Rojhani, “RCS measurements and ISAR images of small UAVs,”
IEEE Aerosp. Electron.Syst. Mag. , vol. 32, no. 9, pp. 28–32, Oct. 2017.[20] C. J. Li and H. Ling, “Wide-angle, ultra-wideband ISAR imaging of vehicles and drones,”
Sensors , vol. 18, no. 10, p.3311, Sept. 2018.[21] Y. Jiang, S. Sun, Y. Yuan, and T. S. Yeo, “Three-dimensional aircraft ISAR imaging based on shipborne radar,”
IEEETrans. Aerosp. Electron. Syst. , vol. 52, no. 5, pp. 2504–2518, Oct. 2016.[22] L. M. Ehrman and W. D. Blair, “Using target RCS when tracking multiple Rayleigh targets,”
IEEE Trans. Aerosp. Electron.Syst. , vol. 46, no. 2, pp. 701–716, May 2010.[23] M. Mertens, M. Ulmke, and W. Koch, “Ground target tracking with RCS estimation based on signal strength measurements,”
IEEE Trans. Aerosp. Electron. Syst. , vol. 52, no. 1, pp. 205–220, Apr. 2016.[24] G. Galati, G. Pavan, and C. Wasserzier, “Characterization of back-scattering and multipath in a suburban area after thecalibration of an X-band commercial radar,”
Sensors , vol. 20, no. 2, pp. 1–19, Jan. 2020.[25] C. J. Bradley, P. J. Collins, J. Fortuny-Guasch, M. L. Hastriter, G. Nesti, A. J. Terzuoli, and K. S. Wilson, “An investigationof bistatic calibration objects,”
IEEE transactions on geoscience and remote sensing , vol. 43, no. 10, pp. 2177–2184, Sept.2005.[26] S. Rahman and D. A. Robertson, “In-flight RCS measurements of drones and birds at K-band and W-band,”
IET RadarSonar Nav. , vol. 13, no. 2, pp. 300–309, Sept. 2018.[27] J. Gong, J. Yan, D. Li, D. Kong, and H. Hu, “Interference of radar detection of drones by birds,”
Prog. Electromagn. Res.(PIER) , vol. 81, pp. 1–11, Apr. 2019.[28] J. Gong, J. Yan, D. Li, and R. Chen, “Using radar signatures to classify bird flight modes between flapping and gliding,”
IEEE Geosci. Remote. Sens. Lett. , vol. 17, no. 9, pp. 1518–1522, Sept. 2019.[29] T. J. Nohara, R. C. Beason, and P. Weber, “Using radar cross-section to enhance situational awareness tools for airportavian radars,”
Human-Wildlife Interactions , vol. 5, no. 2, pp. 210–217, Oct. 2011. [30] R. May, Y. Steinheim, P. Kvaløy, R. Vang, and F. Hanssen, “Performance test and verification of an off-the-shelf automatedavian radar tracking system,” Ecology and evolution , vol. 7, no. 15, pp. 5930–5938, Aug. 2017.[31] ´A. D. de Quevedo, F. I. Urzaiz, J. G. Menoyo, and A. A. L´opez, “Drone detection and radar cross-section measurementsby RAD-DAR,”
IET Radar, Sonar & Navigation , vol. 13, no. 9, pp. 1437–1447, June 2019.[32] R. Nakamura and H. Hadama, “Characteristics of ultra-wideband radar echoes from a drone,”
IEICE Commun. Express ,vol. 6, no. 9, pp. 530–534, June 2017.[33] R. Nakamura, H. Hadama, and A. Kajiwara, “Ultra-wideband radar reflectivity of a drone in millimeter wave band,”
IEICECommun. Express , vol. 7, no. 9, pp. 341–346, July 2018.[34] T. Mizushima, R. Nakamura, and H. Hadama, “Reflection characteristics of ultra-wideband radar echoes from variousdrones in flight,” in
Proc. IEEE WiSNeT, San Antonio, TX , Jan. 2020, pp. 30–33.[35] A. V. Khristenko, M. O. Konovalenko, M. E. Rovkin, V. A. Khlusov, A. V. Marchenko, A. A. Sutulin, and N. D. Malyutin,“Magnitude and spectrum of electromagnetic wave scattered by small quadcopter in X-band,”
IEEE Trans. AntennasPropag. , vol. 66, no. 4, pp. 1977–1984, Apr. 2018.[36] V. Semkin, J. Haarla, T. Pairon, C. Slezak, S. Rangan, V. Viikari, and C. Oestges, “Analyzing radar cross section signaturesof diverse drone models at mmWave frequencies,”
IEEE Access , vol. 8, pp. 48 958–48 969, Mar. 2020.[37] K. T. Selvan and R. Janaswamy, “Fraunhofer and fresnel distances: Unified derivation for aperture antennas.”
IEEE AntennasPropag. Mag. , vol. 59, no. 4, pp. 12–15, 2017.[38] E. F. Knott, J. F. Schaeffer, and M. T. Tulley,
Radar cross section TM -2007 Recommended practice for radar cross-section test procedures,” pp. 1–70, Sept. 2007.[41] A. Lonnqvist, J. Mallat, and A. V. Raisanen, “Phase-hologram-based compact RCS test range at 310 GHz for scale models,” IEEE Trans. Microw. Theory Tech. , vol. 54, no. 6, pp. 2391–2397, June 2006.[42] M. I. Grace, “Measurement of radar cross section using the “VNA master” handheld vna,” http://dl.cdn-anritsu.com/en-us/test-measurement/files/Application-Notes/Application-Note/11410-00604B.pdf, Tech. Rep., July 2011.[43] D. W. Hess, “Introduction to RCS measurements,” in
Proc. IEEE Antennas and Propag. Conf., Loughborough, UK , Mar.2008, pp. 37–44.[44] R. C. Johnson and D. Hess, “Conceptual analysis of measurements on compact ranges,” in
Proc. Antenna ApplicationsSymp., Atlanta, GA , Sept. 1979.[45] H. A. Gaberson, “Applying the inverse FFT for filtering, transient details and resampling,”
J. Sound Vib. , vol. 39, no. 8,pp. 18–23, Aug. 2005.[46] W. T. Beyene and C. Yuan, “An accurate transient analysis of high-speed package interconnects using convolutiontechnique,”
Analog Integr. Circuits Signal Process. , vol. 35, no. 2-3, pp. 107–120, May 2003.[47] P. Schaldenbrand. Window types: Hanning, flattop, uniform, tukey, and exponential. Accessed: 12-27-2020. [Online].Available: https://community.sw.siemens.com/s/article/window-types-hanning-flattop-uniform-tukey-and-exponential[48] V. Borkar, A. Ghosh, R. Singh, and N. Chourasia, “Radar cross-section measurement techniques.”
Defence Science Journal ,vol. 60, no. 2, pp. 204–212, Mar. 2010.[49] C. A. Balanis,
Advanced engineering electromagnetics , 2nd ed. Hoboken, NJ: John Wiley & Sons, Jan. 2012.[50] M. A. Richards, J. Scheer, W. A. Holm, and W. L. Melvin,
Principles of modern radar . Raleigh, NC: SciTech Publishing,Jan. 2010.[51] L. Du, H. Liu, and Z. Bao, “Radar HRRP statistical recognition: parametric model and model selection,”
IEEE Trans. Sig.Proc. , vol. 56, no. 5, pp. 1931–1944, Apr. 2008. [52] Q. Hou, F. Chen, H. Liu, and Z. Bao, “New statistical model for radar hrrp target recognition,” J. Syst. Eng. Electron. ,vol. 21, no. 2, pp. 204–210, Apr. 2010.[53] T. P. Minka, “Estimating a Gamma distribution,”
Microsoft Research, Cambridge, UK, Tech. Rep
Model selection and multi-model inference: a practical information-theoretic approach .New York, USA: Springer-Verlag, Jan. 2002.[55] K. Copsey and A. Webb, “Bayesian gamma mixture model approach to radar target recognition,”
IEEE Trans. Aerosp.Electron. Syst. , vol. 39, no. 4, pp. 1201–1217, Oct. 2003.[56] L. Fischer, B. Hammer, and H. Wersing, “Efficient rejection strategies for prototype-based classification,”
Neurocomputing ,vol. 169, pp. 334–342, Dec. 2015.[57] ——, “Optimal local rejection for classifiers,”